Connection pool saturation under load

Your API tier autoscales beautifully and stays at ~40% CPU through a marketing-driven 3x surge, yet p99 climbs and pool timeout: could not acquire connection within 5000ms errors appear at the app. Each pod has an HTTP client pool to a downstream pricing service sized at 20 connections, a number chosen long ago to match steady-state concurrency. The downstream pricing service itself reports normal latency and is not saturated. Pods are plentiful. How do you triage and mitigate this surge-time failure?